My writing coach through the National Blogging Collaborative is a wonderful woman named Lisa Hollenbach, and I think herÂ getting-to-know-you questionaire is a good tool for thinking about personal and professional goals, so I’m posting my responses here.
Learning, apprenticeship, study.
I’ve mentioned it before, but it’s time to make things Internet-official. I’m stepping out of the classroom next year and taking a leave of absence. I’m excited beyond expression, but I’m also scared. Scared that maybe I’ll never come back or that I’ll realize I was doing things wrong the whole time. Scared that I’ll be away from inspiring educators and remarkable kids who keep me going. Scared that I won’t take full advantage of this opportunity.
Who am I when I’m not a teacher? Am I really going to stop being a teacher when I’m out of the classroom? How can I best improve myself and equip myself to return to a vocationÂ of teaching and learning?
I’m fortunate that the district approved my leave (after sending me a very official piece of certified mail that lookedÂ SO SERIOUS that Toby texted me asking if I was in trouble). I’m fortunate for the Internet so that I won’t be isolated in this year away. I’m fortunate for the support of remarkable friends who help me become a better person. I’m fortunate for administrators whoÂ advocateÂ for the best interests of my students and for the mental health of educators.
Although I’ve been pretty open about my struggles with depression and mania, mental health isn’t the core of why I’m leaving, although I think it does explain why I feel so thoroughly drained and ready for reflection. Teachers leave the profession because they’re burnt out. I hope I’ve caught myself before going over the burnout cliff, and that I will returnÂ to my classroom a more thoughtful and proficient educator.
This week is spring break. I’m working with Toby to craft some sort of framework or schedule so I don’t just sink into a fog of ennui in my bed and never emerge. As first-world-problem as it seems, breaks and vacations are really difficult for me, and it often takes a few weeks into the summer before I stop feeling like my skin is crawling. Routines and schedules help my students, and they help me too. One of my tasksÂ is to write something every day. So here’s my work for today.
Learning, apprenticeship, and study. Those are today’s intentions.
Exit Post-Its for Calculator Mini-Lesson
I try very hard to make my supply list clear, concise, and simple. But I still wind up with kids bringing in calculators and protractors and compasses. I don’t mind students using calculators on many classroom projects, but I do like to have a mini-lesson for appropriate calculator usage before I wind up with students trying to spell out BOOBS on their screens.
I usually answer questions about what the different buttons mean. This year I explained that calculators are often used for finances, so we don’t usually use the percentage key, the square root key, or any of the memory keys. I also clarified that fractions are expressed as decimals on most four-function and scientific calculators.
This year, I had my students jot their learning on a post-it note before we left for lunch. Here are some of their insights, annotated with my responses.
Probably the biggest surprise for me was how many kids had their minds blown by the fact that calculators don’t represent fractions the way we’re used to seeing them in class.
Some students realized the limitations of calculators.
I’m pretty good at deciphering what students are trying to communicate, but if I really can’t understand, I let them know.
Some students focused on the practical expectations we discussed, such as appropriate calculator usage.
And then there were the notes that alerted me that I’d need to follow up with a few students.
The following two students are in their second year with me, so I felt comfortable pushing their thinking further, as well as admitting a lack of mathematical clarity of my use of the word “random.”
I originally taped the post-its to notebook paper so I wouldn’t have random sticky notes floating around my tote bag, but then I took the opportunity to give my kids feedback. What forms do you find useful for exit slips and reflections?
Brush of the Gods Math Lesson Plan
IT’S TIME TO GET ROCKING WITH A LITERATURE-BASED MATH SITUATION!!! Woooooo!!!
Our unofficial-but-kind-of-official district math module recommends starting the year off with understanding multiplying by 0, 1, 2, 5, and 10. It aligns with an Engage NY module and a Georgia module, but I wanted to start our unit off with a problem-based activity to gauge their understanding and to give us an anchor for future learning.
Last week, I read Lenore Look’s magnificent Brush of the Gods, and my kids adored it. Math specialist Siobhan and I plotted a pretty rad activity based on the main character’s huge fresco murals. I’m excerpting some of our lesson in the text of this post, and the whole activity is available for download at the end of the post.
I am posting this activity on a Sunday and I plan on launching this in class tomorrow. So check back in later this week and see what modifications I needed to make on the fly!
Wu Daozi was a legendary muralist and painter who worked in Xian during the Tang Dynasty. I shared these photos from my 2009 trip to Xian (the first two photos in that post are actually from the Forbidden City in Beijing) to provide a sense of scale for the city walls. Then I’ll share this task with my students (it’s explained using the GRASP model for classroom-based assessments / problem-based learning activities).
Wu Daozi Memorial Fresco
- Your task is to create a mural in the fanciful calligraphic style of Wu Daozi. Your mural will be a fresco, using plaster, along with any colored pigments you choose.
- You are an artist inspired by Wu Daozi visiting the Chinese city of Xian.
- Your artwork will be seen by all who travel into, out of, or around the city of Xian. 32.9 million tourists visit Xian every year (http://www.chinatouronline.com/, 2008). The tourism board of Xian needs to know how much your mural will cost in Yuan, the national currency of China.
- The challenge involves designing a mural on a grid. You have one week to submit your design to the tourism board.
Product, Performance, and Purpose
- You will create a mural design, and you will also present a cost analysis of your design. The tourism board of Xian needs to know how much money to budget for the mural, as well as the amount of supplies you will need.
Standards and Criteria for Success
- A successful mural and budget need to include:
- The total cost of your plaster, pigment, and other supplies.
- A breakdown of your costs.
- A mathematical justification of your costs.
- Your mural, designed on grid paper.
- A reflection sharing budget suggestions with aspiring artists.
- Your presentation might include:
- A budget planning sheet.
- Photographs of your budget calculations.
We designed a price sheet that would encourage students to perform repeated addition on numbers they have experience skip counting with.
We also included some items students would need only one of (like the brush), to gauge how they choose to add that toward their total budget.
Siobhan helped me plan a 2nd and 3rd grade rubric with standards from both Common Core mathematical practices and content. Feel free to use these plans however you see fit, but comments are always appreciated so we know how successful things have been in your class!
I acknowledge that there are many other directions I could have taken this activity. I plan on revisiting it later in the year for an area/perimeter situation that BLESSEDLY DOES NOT INVOLVE GARDENS, but for now, my main goal is for students to explore repeated addition and patterns with 0, 1, 2, 5, and 10.
Goodies here! Click click click!Â Brush of the GodsÂ lesson plans & rubrics.
Depth of Understanding in Math
The first few days of school in September are precious. You’re setting the tone of your community, establishing expectations and routines, and keeping your fingers crossed that you’ll be able to squeak some content in along the way.
I’ve noticed that a lot of beginning-of-the-year activities center around literacy. In a sense, that’s fantastic, because high-quality children’s literature has an incredible power to bring people together. But I can’t shake the niggling feeling that yet again, math receives the short end of the stick.
After years of gentle coaxing from colleague Siobhan Chan (you’ll hear plenty about her in the year to come, I assure you), last fall I committed to starting my year using The Art of Problem Solving from Teacher to Teacher. The Teacher to Teacher curriculum has its flaws, and it hasn’t been aligned to our district and state standards in a bajillion years, but I have yet to find a better way to kick off math than with The Art of Problem Solving (I refer to it as AoPS in my lesson plans, but I don’t know if that’s an official acronym).
Last year, I launched AoPS at the same time as Math Minutes (again, a practice not without its flaws, but my students ADORE it, so I’m willing to concede the three minutes of class time it takes, start to finish, including transitions). I struggled with a way to share with my students that although Math Minutes DID place a focus on speed, they couldn’t let it hamper the work they were doing to deeply understand problems. So I came up with this visual:
While explaining it, I used hand motions to indicate that understanding was the biggest, most vital piece of our work in math, then we assure accuracy, then we strive for fluency. It guided our practice throughout the year, and they emerged the most successful class of mathematicians I’ve had in six years.
So this year, based on the success I saw in taking the Gallon Man activity to the next level, I decided to give more ownership to my kids with these three levels of understanding in math. I redid my introduction lesson, providing this as a metaphor:
Understanding: This is the whole ocean. Nothing further can happen until we get here. If we’re not there yet, that’s fine, because at least we know what we’re striving for â€” our understanding is the most critical piece.
Accuracy: Kelp and other seaweed will die if it’s out of the water. Our accuracy is meaningless unless it is grounded in our understanding.
Fluency: If we work on our accuracy in a dedicated way, fish and other critters will come to live among the seaweed. It often happens naturally, but we can use strategies that improve conditions for fluency to flourish.
Then, students created their own representation of the three levels of understanding in their math notebooks. They provided remarkable metaphors, and also gave me insight into their thinking. I’m not really permitted to post student work on a non-district site, but you can view the work of everyone whose parents signed a release at our Artsonia site. So I’ve cropped a lot of these and removed student names, etc.
Many kids drew something very close to my example, which was totally fine.
And some started with my basic example, but took it a step in a different direction. Behold, two representations that take place on the savannah and on a farm, respectively.
And then, some of my students blew my mind. I didn’t have them write their explanations, as this was our first activity of the year and I wasn’t ready for that piece. I did record some of their comments, though.
Although I’m all for partner collaboration and I don’t mind if students’ work is similar, I was concerned that my CLD student (CLD, or Culturally & Linguistically Diverse, is the new, politically correct way to refer to ELL or ESL students) couldn’t explain his picture, while the person sitting next to him had an extremely similar representation and could explain his. This was a signal that I need to follow up with my CLD gentleman.
I’m excited to see what comes up next week in math! I always love comments and suggestions!
Integrating Sound with Math
Time to rethink my integration of science with math. My attempts to connect proportions of the human body with measurement went down in flames in my entry last year, so I’m focusing on Systems, Order, and Organization related to sound this time.
I know sound, math, and science are all suuuuuuper tight. What I don’t know is how to adequately organize my sound unit so it includes great inquiry-based investigations. My guiding framework is an annnnncient curriculum from the National Science Resources Center (published when I was in junior high) that has such profound extension activities as the one featured below:
Ugh. Not helpful. It’s worth noting that there are a whopping two math extension activities in this entire unit.
The wise and enthusiasticÂ Katie Weichert gave me some great ideas to chew on and think about. I wish I saw her more often. But in her absence, I had to get a move on.
So I started trolling the Internet.
This Aztec music lesson seems compelling.
I’m also interested in harmonics, but I don’t know how to build this into a full lesson. My students already use harmonic series as a procedure to line up from music class, so I wouldn’t need to go over the basic musical idea of third and fifth intervals.
THIS could be useful. It appears to be a sound generator. Could I have kids compose a song using fractions and then convert them to their frequencies? Speaking of composing music…
I imagine I could show snippets fromÂ Donald in Mathmagic LandÂ and have students generate questions from that? Yesssssss, I could totally do that… That way the learning would be authentic and related to the curriculum we already have in place!
My only concern remains starting with a video. I want to make sure I’m looking for an introduction that inspires perplexity, not just engagement. After the 27-minute video was released in 1959, Walt Disney admitted:
“The cartoon is a good medium to stimulate interest. We have recently explained mathematics in a film and in that way excited public interest in this very important subject.”
(emphasis is my own) Now in looking at moving from merely interest to investigation…… I suppose that recording student questions will take care of that fear, right? Then having their questions shape the following lessons?
Hmmmmm. Of course, there are a wealth of videos available on sound and math, but much of the information is so complex that I can’t figure out how to simplify it.
I’m also interested in looking at the materials used in instrument strings and the number of strings included in different instruments. How do the number of notes an instrument is capable of producing related to its system? Can systems be different sizes? Is a larger system necessarily “better” or more “complete?”
Anyway. Let’s see how this goes.
When you take time for yourself, good things follow. In this case, it was some REALLY AWESOME MATH.
Friday morning, I missed the bus (oops) and was able to drive to work at a legal speed.
I had an opportunity to drink some nummy nummy coconut mocha coffee and read my Wall Street Journal. And lookie what I found!
The art of the slow-motion soccer goal.
Iâ€™ve been thinking a lot about Dan Meyer commenting on how we spoon feed each step to a problem solving situation, and so today, I went out on a skinny limb and used this graphic to help us work on our measurement skills. I wasn’t sure where our work would take us, but we’re early on in the unit, so many of my students are still working to measure accurately using a ruler.
I showed them the graphic, and Samuel helped me pronounce all the playersâ€™ names. He was our resident expert. Then I opened the floor to mathematical questions.
Hereâ€™s what we brainstormed as our big questions.
Â The questions with green dots to the left are the ones we decided to pursue.
Then, people started asking more â€œnitty-grittyâ€ questions, which we identified as being the â€œquestions along the wayâ€ you had to answer to get to your big ideas. We kept this poster up as we worked. I stayed near my computer so I could capture students’ comments.
â€œYou need to know how big the field is,â€ Savanah spoke up. I handed her my iPad so she could find the field size. She paused. â€œDo I need to know like, how BIG it is or how long the sides are?â€ Â â€œI think youâ€™re asking me whether you need the area or the perimeter?â€ â€œYeahâ€¦ ohhhh, I need the length of the sides.â€ Hereâ€™s the information she found.
After checking another site to verify the accuracy of her information, we added the dimensions of the field to the poster. (Yes, I know I could have taken a screen shot of the iPad, and I did, but I couldn’t get the image sent to my computer. Hrmph.)
â€œBut whatâ€™s a yard?â€ â€œWho can answer that?â€ â€œItâ€™s three feet,â€ Ivy answered. â€œHow can you check to see if you agree?â€ â€œWell, I could look in my math book, but I remember what yard sticks last year look like, and I know there are three rulers.â€ (I knew we’d need to convert from yards to feet to inches so they’d be able to convert the lengths they measured on their papers into the actual lengths)
â€œWell, then you need to multiply by three to get the length â€“ 120 times three.â€ â€œWoah. Howâ€™re we going to do that?â€ â€œUse a known fact, 12 x 3.â€ â€œ36?â€ â€œYeah, 36.â€ â€œSo itâ€™s 360 feet.â€
They did the same for the other side. Then a group of students wanted to determine the linear distance the ball traveled for each player. I asked how many inches long their picture was, and Marcos stopped us all.
Marcos: WAIT. You blew up the picture from your newspaper article. So our picture isnâ€™t the same size as yours and the distances will be all different. (I photocopied the graphic at 121% so it’d be easier to read than my original copy of the newspaper.)
Me: Nice. That would be a problem if the image were STRETCHED like a rubber band and warped, but since it was enlarged to scale, weâ€™ll be okay AS LONG AS you donâ€™t let me use my original copy, okay?â€
Marcos: Okay. So the field is 11 inches long.
“You know, if they would have just included a map scale on this picture, we wouldn’t have to do ANY of this measurement.” “I guess that’s why Miz Houghton wants us to be able to use map scales in social studies.”
Then a few of us worked to create this poster.
We knew the field was 11 inches in our image, but we wanted to know how far just ONE inch would be because then we could find out how far Jone Samuelson’s 6-inch kick actually went. We also knew how long an actual field was, so we tried to find the relationship between the two.
Using a fact family (the triangle drawn above) helped us figure out the ratio. Or. What I initially THOUGHT was the ratio. DO YOU SEE MY GLARING ERROR??? I didnâ€™t notice until lunch. I neglected to convert the 240 feet into inches so the units matched. Drat. I frantically called AP Calculus teacher James Brown to make sure I didn’t make any further errors.
So after lunch we converted 240 feet into inches, THEN used the ratio and found out that one inch in our picture equalled approximately 33 feet.
Some students switched to using calculators for these larger computations, which gave us a chance to talk about how calculators represent 1/2, equivalent fractions (5/10), etc. Above, Alejandra calculated how many feet David Villa kicked the ball (5 inches, according to her measurements, making the kick 165 feet). I asked her about the “33 in. in a inch” she wrote, and she said, “Oh no no no, it’s not 33 INCHES or that would be like a mini soccer field.” So she was also looking at reasonableness of answers.
Another group wanted to know how far the balls would have gone if they were kicked on the moon. Again, I told them to ignore the parabolic motion and just look at linear distance. I know the physics of this arenâ€™t entirely correct, but I didnâ€™t think itÂ hurt the integrity of the original problem situation.
Oh, actually! Selam originally asked how far the ball would go in SPACE, but Maya pointed out that if the they were in space, the player and ball would both push off each other and the ball would never land (AMAZING INSIGHT, RIGHT???). So we clarified that the ball would be kicked on the moon, where there was still a force acting on the ball, but a lesser force than what we’d find on Earth.
Adam went to the classroom library to find out what the gravity was on the moon. Hereâ€™s the passage he found, from the DK Eyewitness Book UNIVERSE.
Eayn: It says the gravity is one-sixths of Earth!
Me: So the gravity is 1/6 of the gravity on the Earth. So if we are converting from the moon, what would we have to do to the distance we calculated for the ball kicked on Earth?
Adam: Multiply it by three?
Me: Where did you get three from?
Adam: I dunno.
Milena: Multiply it times five.
Me: Five? Where did you get that from?
Milena: If the moonâ€™s gravity is 1/6, then the rest of the fraction thatâ€™s left is 5/6.
Me: Ohhh, I think I see what youâ€™re picturing in your head. But think of the gravity on the Earth as being one whole, and the gravity on the moon being 1/6 of that whole. You’re not looking at the other 5/6ths.
Vy: Youâ€™d multiply it times six.
Me: Where did you get six from?
Vy: If itâ€™s dividing by six to get the pull on the moon, then youâ€™d multiply by six to show how much further the ball would go when it has a sixth of the gravity slowing it dowwn.
Me: So youâ€™re saying that fractions can be a way of dividing.
Vy: Yep. And then the opposite, er, inverse, is multiplying, so you times by 6.
(It is perhaps worth noting that Vy has not voluntarily spoken in front of the class in the past year and two months)
Wow. So now that we knew how to find distances on Earth and on the moon, we plugged away, with at least three people needing to agree on their measurements to the nearest half-inch before we would post the results. (reviewing our estimation and rounding unit from earlier in the year)
As we approached second recess, we posted what we’d come up with so far.
We also reflected on what we’d learned over the course of the day, and on the math we used.
As you can see, we didn’t finish everything, so some students asked if they could finish the calculations during Math Daily Five. UM, YES OF COURSE.
What suggestions or modifications do you have to offer me and my students? Where can we take things from here? Other thoughts?
I arrived in Dallas yesterday evening.
This is an enormous city. I flew into the airport featured in Gila Monsters Meet You At The Airport. It is an enormous airport. I was met, not by a gila monster, but by the lovely educator-history-buff-museum-gal ElainaÂ (Hauk) Carlisle, who I’ve known through MSU-genius-friend-and-roommateÂ Franny Howes for close to ten years, but have never met in person. She has a fantastic house with epically tall ceilings and a friendly, happy mutt who looks like a Muppet. And a husband, who is accustomed to lengthy teacher-talk conversations.
We drove through Dallas. I saw the place where John F. Kennedy was shot, which is frankly still giving me extreme feelings related to creepiness and the power and gravity of history and all sorts of other random emotions. Yes, I saw the grassy knoll (it’s small). Yes, I saw the book depository (it’s ordinary). I am still processing how such a short glimpse â€” we literally just drove through the intersection, not stopping â€” of an historical site can have such a big impact.
WE ATE DELICIOUS FOOD. Lockhart Smokehouse is close to my hotel, so it was a perfect choice. A DELICIOUS CHOICE.
Then I came home, reserved my Wednesday shuttle to the convention center, and fell into bed to read The Adventures of Sherlock Holmes.
I’m trying to be reflective and thoughtful about tomorrow’s presentation without freaking myself out. I’ve been only marginally successful.
My most significant crisis of confidence came this morning, when I sat up in bed (or rather, flopped over in bed, pushing the aforementioned Sherlock Holmes volume off me) and said, “I can’t possibly read a book as a part of my freaking session; no one’s going to sit around and hear a whole book!”
I fretted. But I reread the speakers’ notes and focused on this bit, “Your presentation method should be consistent with and model strategies that NCTM advocates for classroom teaching (Example: Principles and Standards for School Mathematics).” Hm.
We’re always complaining about math standards going a mile wide and an inch deep, right? So I got myself in check. What better way to demonstrate the importance of deeper understanding by anchoring this brief (hour-long) session around one common text? After all, I told myself, THE TITLE OF MY FREAKING PRESENTATION IS DEEPENING LITERATURE CONNECTIONS. I mean, this way, even if they hate my presentation and the strategies presented, they’ll be able to bring news of a fantastic new picture book back to their schools.
So I’m sticking with sharing Extra Yarn and using it to illustrate how the language of teaching comprehension strategies used in literacy can be math. I’m sharing student-derived examples of how math can be taken from the book. People will be able to try out their own problems and I’ll post them on this site.
Additionally, I found this part of my speakers’ email useful:
New this year! Attendees will have the opportunity to rate presentations using the survey on the Dallas Conference App.
Using a 1-5 scale attendees will rate the following:
â€¢ Overall rating of session
â€¢ Presenterâ€™s knowledge and understanding of the topic.
â€¢ Presenterâ€™s use of appropriate and effective teaching and learning strategies
â€¢ Likelihood of attending another session by this presenter. (Yes/no/maybe)
I know I won’t be able to please everybody with my presentation, but JUST LIKE WITH OUR KIDS, it’s so helpful to know what I need to do with the end goal in mind, so seeing what I’m going to be rated on helps me narrow my mind from the bloom of concerns that are crowding each other out in my brain.
One last worry that remains is that I’m breaking copyright laws by projecting Extra Yarn. But… a picture book read-aloud isn’t a freaking copyright violation, is it? Lawd help us if it is.
Oh, also, I’ve been working to make sure I won’t be doing emphatic karate-chop gestures all presentation long.
Anyway. Enough. Time for lunch and reading.
3rd Grade Geometry Unit Practice
After the positive reception from my students about our Uno’s Garden review activity for estimation and multiplication, I decided to create a similar activity to practice the skills from our geometry unit.
You can see our district power standards here. I’ve modeled the activity directly from the state standards, though, because there are a few holes. Also, looking to the future, here are the geometry Common Core standards. I linked each of the problems to Barbara Kerley’s great biography, What to do About Alice?
We’d been reading So You Want to be President, and I remembered this image from Kerley’s book:
The couch! We could find the perimeter of the couch! So I developed a set of six questions related to the book, posted them around the room, and had students move from question to question at their own pace. Because we’re a 2nd/3rd grade class, there are questions at a variety of difficulty and depth of knowledge to permit everyone some successes.
You can see the questions and my answer booklet below (I always print it on special paper because students have told me it makes the activity feel more like a quest or a scavenger hunt rather than just skills practice).
Please let me know if you found this lesson useful! I’ve found it to be a much better alternative to a straight-up assessment.
Book of the Week: Mathematickles!
Every Monday, I highlight a book from our school bookroom along with lesson plan suggestions. I hope you find this useful, and please leave a comment with any suggestions or additions!
Mathematickles!, by Betsy Franco
I feel like I’ve already written a post about this book, but I can’t seem to find a draft anywhere, so I’ll start again.
Poet Betsy Franco has recently received attention for her duo of domesticated animal books. A Curious Collection of Cats received some Caldecott buzz after it was published, and of course you know I’m cat biased, but I didn’t think A Dazzling Display of Dogs was quite as good as a followup.
Anyway, back to Mathematickles. As usual, there are plenty of great math lessons available that tie into this book.Â For example, you should definitely do this lesson.Â It has the added benefit of relating math to the seasons, and I plan to use this book to reinforce inverse operations for multiplication/division and solving for a missing addend.
There is aÂ CAFE menuÂ included with this mentor text, and Iâ€™ve highlighted these as suggested lessons:
- Recognize literary elements (figurative language). The book’s equations sometimes work due to literal language (like 1/2w = v = flying geese) and sometimes due to figurative language (such as raindrops x leaves = pearls on green plates). Due to the limited text in the book, it’d be pretty easy to copy several (dare I say all?) the poems an have students sort for the two elements.
- Use dictionaries, thesauruses and glossaries as tools. If some of the math terms or symbols are unfamiliar, students can use the glossaries in the back of their math textbooks. There are plenty of terms also available at the online dictionary MathWords.
Behaviors that Support Reading
- Read the whole time. As mentioned, this book doesn’t have very much text. So how can students make sure they’re reading the entire time, especially if they have lower-level books with limited words on each page? Brainstorm student ideas and post them in the room.
Please add any lessons or supplemental materials to the book bag so future teachers can utilize your good thinking!
Comments and constructive feedback are always welcomed. Please let me know if these lessons were useful in your class!